I think it has something to do with heat transfer. Whether something feels cold or warm depends on how well it transfers heat. So air is pretty good at transferring heat. A cup of coffee will quickly get cold if you put i outside, as the air is much cooler that the coffee, and so will take the heat away.
Water is even better at taking heat away than air, so if you go into the water, it will suck out your body heat even faster than the air, even if it is the same temperature as the air. That is what feels cold. This also the reason why e.g., iron feels colder than wood, because it transfers heat much better.
Fun fact: Evaporation transfers heat even better than water. That is why it can feel even colder when you leave the water and are wet, than it felt down in the water, because the water evaporates from your body.
Feel free to correct me if i am wrong, im a philosopher, not a phycisist 🙂
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